Question

Un triunghi dreptunghic are aria 210 centimetri patrati si ipotenuza de 29 cm.Calculati lungimile catetelor triunghiului.

Answer 1

Notam triunghiul ABC
AD_I_BC
A=210
29x h/2=210
h=420/29
notamBD=x
DC=29-x
AB²=√29x
AC²=√29(29-x)
√29x ×√29(29-x) /2=210
√29x ×29(29-x) =420
24389x-841x²=176400
24389x-841x²=176400
841x²-24389x+176400=0
Δ=24389²-4×841×176400=1413721
√1413721=1189
BD=x₁=(24389+1189)/2×841=441/29
DC=x₂=(24389-1189)/2×841=400/29
AB=√29 ×441/29 =√441=21 cm
AC=√29 ×400/29 =√400=20 cm